Measurements of stellar orbits provide compelling evidence that the compact radio source SgrA* at the Galactic Centre is a 4 million solar mass black hole. With the exception of modest X-ray and infrared flares, SgrA* is surprisingly faint, suggesting that the accretion rate and radiation efficiency near the event horizon are currently very low. I will discuss the surprising recent detection of a dense, approximately 3 Earth mass gas cloud that is falling on a near-parabolic orbit into SgrA*'s accretion zone. Our adaptive optics infrared observations with the ESO VLT tightly constrain the cloud's orbit with an innermost radius of approach of only ~3100 times the event horizon in 2013. Over the past three years the cloud has begun to disrupt, probably mainly by tidal shearing due to the black hole's gravitational force. The cloud's dynamic evolution and radiation in the next years will probe the properties of the accretion flow and the feeding processes of the super-massive black hole. The keV X-ray emission of SgrA* may brighten significantly when the cloud reaches pericenter. There may also be a giant radiation flare several years from now if the cloud suffers breakup with its fragments feeding gas into the central accretion zone. I will discuss two scenarios how this cloud might have been created.